2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/58476We construct a functor from the derived category of homotopy Gerstenhaber algebras with finite-dimensional cohomology to the purely geometric category of so-called $F_{\infty}$-manifolds. The latter contains Frobenius manifolds as a subcategory (so that a pointed Frobenius manifold is itself a homotopy Gerstenhaber algebra). If a homotopy Gerstenhaber algebra happens to be formal as a $L_{\infty}$-algebra, then its $F_{\infty}$-manifold comes equipped with the Gauss-Manin connection. Mirror Symmetry implications are discussed.More details on the relationship between formality maps and Gauus-Manin connections are given in Sect.2.7Algebraic GeometryDifferential Geometrytext